Abstract: Differential evolution (DE) is one of the most powerful stochastic search methods which was introduced originally for continuous optimization. In this sense, it is of low efficiency in dealing with discrete problems. In this paper we try to cover this deficiency through introducing a new version of DE algorithm, particularly designed for binary optimization. It is well-known that in its original form, DE maintains a differential mutation, a crossover and a selection operator for optimizing non-linear continuous functions. Therefore, developing the new binary version of DE algorithm, calls for introducing operators having the major characteristics of the original ones and being respondent to the structure of binary optimization problems. Using a measure of dissimilarity between binary vectors, we propose a differential mutation operator that works in continuous space while its consequence is used in the construction of the complete solution in binary space. This approach essentially enables us to utilize the structural knowledge of the problem through heuristic procedures, during the construction of the new solution. To verify effectiveness of our approach, we choose the uncapacitated facility location problem (UFLP)--one of the most frequently encountered binary optimization problems--and solve benchmark suites collected from OR-Library. Extensive computational experiments are carried out to find out the behavior of our algorithm under various setting of the control parameters and also to measure how well it competes with other state of the art binary optimization algorithms. Beside UFLP, we also investigate the suitably of our approach for optimizing numerical functions. We select a number of well-known functions on which we compare the performance of our approach with different binary optimization algorithms. Results testify that our approach is very efficient and can be regarded as a promising method for solving wide class of binary optimization problems.

Abstract: In this paper, we consider approximation algorithms for optimizing a generic multivariate polynomial function in discrete (typically binary) variables. Such models have natural applications in graph theory, neural networks, error-correcting codes, among many others. In particular, we focus on three types of optimization models: (1) maximizing a homogeneous polynomial function in binary variables; (2) maximizing a homogeneous polynomial function in binary variables, mixed with variables under spherical constraints; (3) maximizing an inhomogeneous polynomial function in binary variables. We propose polynomial-time randomized approximation algorithms for such polynomial optimization models, and establish the approximation ratios (or relative approximation ratios whenever appropriate) for the proposed algorithms. Some examples of applications for these models and algorithms are discussed as well.

Abstract: This paper presents a unified framework for intra-view and inter-view constraint propagation on multiview data. Pairwise constraint propagation has been studied extensively, where each pairwise constraint is defined over a pair of data points from a single view. In contrast, very little attention has been paid to interview constraint propagation, which is more challenging since each pairwise constraint is now defined over a pair of data points from different views. Although both intraview and inter-view constraint propagation are crucial for multi-view tasks, most previous methods can not handle them simultaneously. To address this challenging issue, we propose to decompose these two types of constraint propagation into semi-supervised learning subproblems so that they can be uniformly solved based on the traditional label propagation techniques. To further integrate them into a unified framework, we utilize the results of intra-view constraint propagation to adjust the similarity matrix of each view and then perform inter-view constraint propagation with the adjusted similarity matrices. The experimental results in cross-view retrieval have shown the superior performance of our unified constraint propagation.

Abstract: In constraint-based programming, robot tasks are specified and solved as optimization problems with sets of constraints and one or multiple objective functions. In our previous work, we presented (i) a generic modeling approach for geometrically complex robot tasks, including the modeling of parametric uncertainty, in order to allow the robot task programmer to specify the optimization problem without explicitly writing down the different (possibly numerous and involved) constraint equations, and (ii) methods for solving these optimization problem online in the instantaneous case (reactive control), and offline in the non-instantaneous case (trajectory planning). This paper has two contributions. First, it extends our framework to include task constraints (e.g. tracking a curve) that are not given as explicit functions of time. These constraints are highly relevant in practice, for example to facilitate time-optimal path planning combined with other constraints. Second, it extends our framework to user-configurable task horizons when solving the optimization problem, to allow task programmers to make a trade-off between computational speed and (global) task optimality. Both of these novel framework extensions are illustrated by a time-optimal laser tracing experiment.

Abstract: In Constraint Programming, constraint propagation is a basic component of constraint satisfaction solvers. Here we study constraint propagation as a basic form of inference in the context of first-order logic (FO) and extensions with inductive definitions (FO(ID)) and aggregates (FO(AGG)). In a first, semantic approach, a theory of propagators and constraint propagation is developed for theories in the context of three-valued interpretations. We present an algorithm with polynomial-time data complexity. We show that constraint propagation in this manner can be represented by a datalog program. In a second, symbolic approach, the semantic algorithm is lifted to a constraint propagation algorithm in symbolic structures, symbolic representations of classes of structures. The third part of the article is an overview of existing and potential applications of constraint propagation for model generation, grounding, interactive search problems, approximate methods for ∃∀SO problems, and approximate query answering in incomplete databases.

Abstract: Constraints can render a numerical optimization problem much more difficult to address. In many real-world optimization applications, however, such constraints are not explicitly given. Instead, one has access to some kind of a "black-box" that represents the (unknown) constraint function. Recently, we proposed a fast linear constraint estimator that was based on binary search. This paper extends these results by (a) providing an alternative scheme that resorts to the effective use of support vector machines and by (b) addressing the more general task of non-linear decision boundaries. In particular, we make use of active learning strategies from the field of machine learning to select reasonable training points for the recurrent application of the classifier. We compare both constraint estimation schemes on linear and non-linear constraint functions, and depict opportunities and pitfalls concerning the effective integration of such models into a global optimization process.

Abstract: In global optimization with evolutionary algorithms constraint handling presents major difficulties, especially in the case of equality constraints. Several techniques have been proposed to overcome this difficulty. In this work an adaptive constraint handling technique is studied on a set of test problems with two evolutionary algorithms. The results indicate that the proposed adaptive technique produces results with better quality in terms of objective function values and constraint violations. The comparison was assessed by performance profiles based on a new metric that considers information both on objective function value and constraints violation.

Abstract: In this paper, we consider a globally optimal design of IIR filters. We formulate the design problem as a nonconvex optimization problem with a continuous inequality constraint and a nonconvex constraint. To solve this problem, the constraint transcription method is applied to tackle the continuous inequality constraint. In order to avoid the obtained solution being on the boundary of the feasible set, more than one initial points are used. Moreover, since the objective and the constraints are nonconvex functions, there may be many local minima. To address this problem, the filled function method is applied to escape from the local minima. Some numerical computer simulation results are presented to illustrate the effectiveness and efficiency of the proposed method.

Abstract: The holy grail of constrained optimization is the development of an efficient, scale invariant and generic constraint handling procedure in single and multi-objective constrained optimization problems. In this paper, an individual penalty parameter based methodology is proposed to solve constrained optimization problems. The individual penalty parameter approach is a hybridization between an evolutionary method, which is responsible for estimation of penalty parameters for each constraint and the initial solution for local search. However the classical penalty function approach is used for its convergence property. The aforesaid method adaptively estimates penalty parameters linked with each constraint and it can handle any number of constraints. The method is tested over multiple runs on six mathematical test problems and a engineering design problem to verify its efficacy. The function evaluations and obtained solutions of the proposed approach is compared with three of our previous results. In addition to that, the results are also verified with some standard methods taken from literature. The results show that our method is very efficient compared to some recently developed methods.

Abstract: We present an n-ary constraint for the stable marriage problem This constraint acts between two sets of integer variables where the domains of those variables represent preferences Our constraint enforces stability and disallows bigamy For a stable marriage instance with $n$ men and $n$ women we require only one of these constraints, and the complexity of enforcing arc-consistency is $O(n^2)$ which is optimal in the size of input Our computational studies show that our n-ary constraint is significantly faster and more space efficient than the encodings presented in \cite{cp01} We also introduce a new problem to the constraint community, the sex-equal stable marriage problem

Abstract: Evolutionary algorithms are a popular choice for solving multi-disciplinary optimization problems as they are simple to use and are widely applicable. However, such algorithms require numerous function evaluations prior to its convergence. In the context of constrained optimization (i.e. a vast majority of real life problems), such algorithms use some sort of constraint violation (CV) measure to rank infeasible solutions in the population. Existing algorithms compute such constraint violation measure by evaluating all constraints of the problem. If the user is only interested in the final set of feasible solutions (i.e. Pareto solutions), such an approach can be questioned as “what is the worth of evaluating subsequent constraints when the solution has already violated at least once ?”. This question becomes even more relevant and important in the event if evaluation of such constraints is computationally expensive or the problem involves many constraints. Based on the above motivation, an algorithm is designed using the framework of differential evolution. The population is divided into multiple sub-populations and each sub-population is assigned a prescribed constraint sequence. In any sub-population, evaluation of a solution is aborted whenever it violates a constraint. Such a strategy allows the population to approach the feasible space from different directions, thereby offering a greater chance to reach the Pareto front. The benefits of such a sequencing approach are illustrated using an example before illustrating its performance across a number of engineering design optimization problems. The results of the proposed approach are compared with NSGA-II and the same differential evolution algorithm relying on constraint violation measure derived through evaluation of all its constraints. The results clearly indicate, that the approach is able to identify the first feasible solution earlier than other approaches and often has a greater diversity which in turn results in a better non-dominated set of solutions.

Abstract: We present a new approach to constrained quadratic binary programming. Dual bounds are computed by choosing appropriate global underestimators of the objective function that are separable but not necessarily convex. Using the binary constraint on the variables, the minimization of this separable underestimator can be reduced to a linear minimization problem over the same set of feasible vectors. For most combinatorial optimization problems, the linear version is considerably easier than the quadratic version. We explain how to embed this approach into a branch-and-bound algorithm and present experimental results.

Abstract: Many important computational problems may be formulated as constraint satisfaction problems (CSP). In this paper, we propose a new approach to solve the binary CSP problems using the continuous Hopfield networks (CHN). This approach is divided into three steps: the first concerns reducing the size of the CSP problems using arc consistency technique AC3. The second step involves modeling the filtered constraint satisfaction problems as 0-1 quadratic programming subject to linear constraints. The last step concerns applying the continuous Hopfield networks to solve the obtained 0-1 optimization model. Therefore, the mapping procedure and an appropriate parameter setting procedure about CSP problems are given in detail. Finally, some computational experiments solving the CSP problems are shown.

Abstract: Many real-life problems are over-constrained, so that no solution satisfying all their constraints exists. Soft constraints, with costs denoting how much the constraints are violated, are used to solve these problems. We use the edit-distance based SoftRegular constraint as an example to show that a propagation algorithm that sometimes underestimates the cost may guide the search to incorrect (non-optimal) solutions to an over-constrained problem. To compute correctly the cost for the edit-distance based SoftRegular constraint, we present a quadratic-time propagation algorithm based on dynamic programming and a proof of its correctness. We also give an improved propagation algorithm using an idea of computing the edit distance between two strings, which may also be applied to other constraints with propagators based on dynamic programming. The asymptotic time complexity of our improved propagator is always at least as good as the one of our quadratic-time propagator, but significantly better when the edit distance is small. Our propagators achieve domain consistency on the problem variables and bounds consistency on the cost variable. Our method can also be adapted for the violation measure of the edit-distance based Regular constraint for constraint-based local search.

Abstract: In this paper a Basic Constraint Qualification is introduced for a nonconvex infinite-dimensional vector optimization problem extending the usual one from convex programming assuming the Hadamard differentiability of the maps. Corresponding KKT conditions are established by considering a decoupling of the constraint cone into half-spaces. This extension leads to generalized KKT conditions which are finer than the usual abstract multiplier rule. A second constraint qualification expressed directly in terms of the data is also introduced, which allows us to compute the contingent cone to the feasible set and, as a consequence, it is proven that this condition is a particular case of the first one. Relationship with other constraint qualifications in infinite-dimensional vector optimization, specially with the Kurcyuscz-Robinson-Zowe constraint qualification, are also given.

Abstract: Sparse clustering, which aims at finding a proper partition of extremely high dimensional data set with fewest relevant features, has been attracted more and more attention. Most researches model the problem through minimizing weighted feature contributions subject to a l1 constraint. However, the l0 constraint is the essential constraint for sparse modeling while the l1 constraint is only a convex relaxation of it. In this article, we bridge the gap between the l0 constraint and the l1 constraint through development of two new sparse clustering models, which are the sparse k-means with the lq(0 <; q <; 1) constraint and the sparse k-means with the l0 constraint. By proving the certain forms of the optimal solution of particular lq(0 = q <; 1) non-convex optimizations, two efficient iterative algorithms are proposed. We conclude with experiments on both synthetic data and the Allen Developing on both synthetic data and the lq(0 = q <; 1) models exhibit the advantages compared with the standard k-mans and sparse k-means with the l1 constraint.

Abstract: This is a summary of the journal article (Malapert et al. 2012) published by Journal on Computing entitled "An Optimal Constraint Programming Approach to the Open-Shop Problem". The article presents an optimal constraint programming approach for the Open-Shop scheduling problem, which integrates recent constraint propagation and branching techniques with new upper bound heuristics. Randomized restart policies combined with nogood recording allow to search diversification and learning from restarts. This approach is compared with the best-known metaheuristics and exact algorithms, and shows better results on a wide range of benchmark instances.

Abstract: The FOCUS constraint expresses the notion that solutions are concentrated In practice, this constraint suffers from the rigidity of its semantics To tackle this issue, we propose three generalizations of the FOCUS constraint We provide for each one a complete filtering algorithm as well as discussing decompositions

Abstract: An improved constraint handling technique based on a comparison mechanism is presented, and then it is combined with selection operator in differential evolution to fulfill constraint handling and selection simultaneously. A differential evolution with two mutation strategies based on this new constraint handling technique is developed to solve the linear bilevel programming problems. The simulation results show that the proposed algorithm can find global optimal solutions with less computation burden.

Abstract: One of the most important logic constraints is the constraint of difference. It is imposed on a set of discrete variables requiring that they receive pairwise distinct values. This construct, initially studied in the field of Artificial Intelligence (in particular, Constraint Programming), has numerous applications and important theoretical properties. In the current work, we show that the polytope associated with this constraint is a generalized polymatroid and thus totally dual integral. As a consequence the problem of optimizing a linear function when variables are restricted to take pairwise distinct values belongs to P. Furthermore, we prove that the above problem can be solved by the greedy algorithm in O(|J| · log|J|) steps where J denotes the set indexing the variables (to receive pairwise distinct values). We establish that the dual of the above problem can also be solved in the same number of steps.

Abstract: Constraint diagrams were proposed as a means of modelling software systems, with generalized constraint diagrams being a recent refinement. It is known that generalized constraint diagrams are more expressive than constraint diagrams and can express any first-order logic statement that uses monadic or dyadic predicates. Thus, the generalized constraint diagram logic is undecidable. In this article, we develop a decision procedure for the so-called existential fragment of generalized constraint diagrams, building on previous work for a simpler, less expressive, fragment of the logic.

Abstract: We consider the problem of boolean compressed sensing, which is also known as group testing. The goal is to recover a small number of defective items in a large set from a few collective binary tests. This problem can be formulated as a binary linear program, which is NP hard in general. To overcome the computational burden, it was recently proposed to relax the binary constraint on the variables, and apply a rounding to the solution of the relaxed linear program. In this paper, we introduce a randomized algorithm to replace the rounding procedure. We show that the proposed algorithm considerably improves the success rate with only a slight increase in computational cost.

Abstract: The topology optimization design problem with multiple constraints for the complex vertical tail structure is studied in this paper The variable density structural topology optimization method is improved by introducing a constraint factor According to the different structural constraints and design requirements, variable factors and element pseudo density are initialized via finite element method This method is controlled by the constraint factors, and the improved method combining with Rational Approximation of Material Properties (RAMP) density-stiffness interpolation model with optimality criteria methods (OC), the vertical tail’s stiffness optimization has been finished The density-stiffness interpolation model, the mathematical model of variable density method with constraint factor, the structural optimization model, the solution model of the OC method, the design variables iterative format, are given in this paper and the algorithm with Matlab program is realized Lastly, a sample vertical tail case is introduced to validate the feasibility of the algorithm by operating the results and analyzing the data

Abstract: Portfolio selection is a relevant problem in finance and economics. It consists in selecting a portfolio of assets considering a given expected return such that the risk of the portfolio is minimized. Several approaches have been proposed to tackle this problem, which are mainly based on mathematical programming techniques and metaheuristics. In this paper we illustrate how this problem can easily be modeled and solved by a relatively modern and declarative programming paradigm called constraint programming.

Abstract: This paper proposes the use of binary trees in order to represent and evaluate asymmetric decision problems with Influence Diagrams (IDs). Constraint rules are used to represent the asymmetries between the variables of the ID. These rules and the potentials involved in IDs will be represented using binary trees. The application of these rules can reduce the size of the potentials of the ID. As a consequence the efficiency of the inference algorithms will be improved.